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We  have  this  equation

total wins                        [ 2  +  2n ]

_________     =             __________  =    .60    

total games                    [ 15  + 3n ]

Where n  is the  number of weeks  after  the  5th week

Multiply  both sides  by   15 + 3n  and we have that

2 + 2n   =   .60 [15 + 3n ]  

2 + 2n  =  9  + 1.8n      subtract  1.8n, 2  from both sides

.2n = 7      divide  both sides  by  .2

n =  35

So..it will take   5 + n =  5 + 35 =   40 weeks to reach a  60%  winning percentage

Proof:

After   40  weeks  we  have   2 + 2(35)  =   72 wins

And  15 + 3(35)  =  120  games will have been played

So

72  / 120    =   .60

Cphill, melody, or geno3141 PLEASE HELP!!! (I am depending on you guys becuase you are one of the smartest people ive ever known.)

THANK YOU SO MUCH IF YOU CAN HELP!!!

First  one :

Coordinates  of  A '   =  (1,2)

Second one :

Coordinates of B '  = (2, 5)

Third  one :

Coordinates  of C'   = (4, -3)

Note  that the  rule for a 180°  rotation  seems to  be :

(x , y)  ⇒  ( -x, - y)

Jason jumped off a cliff into the ocean while vacationing with some friends. His height as a function of time could be modeled by the function h(t)= -16t^2 + 16t + 480, where t is the time in seconds and h is the height is feet.

a. How long did it take for Jason to reach his maximum height?

The  time  to  reach  the max  height is given by :

-16/ [ 2 * -16]  =  1 / 2  sec

b. What was the highest point that Jason reached?

Highest point  =  -16(1/2)^2  + 16 (1/2) + 480  =  -4 + 8 + 480  =  484  ft

c. Jason hit the water after how many seconds?

We need to solve  this :

-16t^2 + 16t  + 480  = 0         divide throug  by  - 16

t^2  -  t   -  30 =   0      factor

(t + 5) ( t - 6)    = 0

Seteting each factor to 0  and solving for  t  produces

t  =  - 5 sec  [ reject ]

or

t = 6 sec   [ accept ]

First  one  ⇒  point   L

Second  one ⇒  point B

Third one......  reflection over  the  x  axis rule  :  ( x , y)  ⇒  (  x ,-y) 

So

(2, 1)  ⇒ (2, - 1)

CORRECT   !!!

Let's see if  any pattern "falls out"

[0 + 1 ] / 3    =   1    =      F₍₂₎

[ 1 + 1]  / 3    =  2   =       F₍₃₎

[ 1 + 2 ]  / 3    = 0   =       F₍₄₎

[ 2 + 0 ] / 3     = 2   =       F₍₅₎

[ 0 + 2 ] / 3     = 2   =       F₍₆₎

[ 2 + 2] / 3     =  1   =       F₍₇₎

[ 2+ 1 ] / 3      = 0   =       F₍₈₎

[ 1 + 0 ] / 3    =  1    =      F₍₉₎

[ 0  + 1]  / 3  =   1    =      F₍₁₀₎   

[ 1  + 1] / 3 =     2   =       F₍₁₁₎   

[ 1 + 2 ]  / 3  =   0    =      F₍₁₂₎   

[ 2 + 0 ] / 3   =   2     =     F₍₁₃₎

[ 0 + 2]  / 3   =   2    =      F₍₁₄₎

[2 + 2 ] / 3    =   1    =      F₍₁₅₎

[ 2  + 1] / 3   =  0    =       F₍₁₆₎

[ 1 + 0] / 3  =    1  =         F₍₁₇₎

Note  that  the pattern  has  a  cycle of  8

And  the cycle  starts at  the indexes   2 , 10  , 18,  26  ...etc.

So  the pattern begins  repeats  for  every [-6 + 8n ] th   index  number

And  note  that 

-6 + 8(253)  =  2018

So  this means that

F₍₂₀₁₈₎    begins the  253nd  cycle  

So  this  must  mean  that

F₍₂₀₁₇₎   =   1    [  the last remainder  in the  252nd cycle ] 

F₍₂₀₁₈₎   =   1

F₍₂₀₁₉₎   =   2

F₍₂₀₂₀₎   =   0

F₍₂₀₂₁₎    =  2

F₍₂₀₂₂₎   =   2

F₍₂₀₂₃₎   =   1

F₍₂₀₂₄)   =   0

And  the  sum of these remainders    =   9

It's 65

The closest to B

it is -9

We have this system :

V +  B  =   15     ⇒   V =  15  - B     (1)

7V  +  25B  =   231       (2)

Sub  (1)  into (2)  for  V   and we  have that

7 (15 - B)  + 25B  = 231   simplify

105 - 7B + 25B  =  231

105 +18B =  231     subtract 105  from each side

18B = 126     divide  both sides  by  18

B =  7  (buses)

V =15 - 7  =   8 (vans)

We have this system  :

3B  + 2H  = 19      multiply  through by - 2    ⇒  -6B - 4H  = -38    (1) 

6B + 5H =  40    (2)

Add (1)  and (2)   and we  get that

 H  =   2     ⇒  [ a hot dog  costs $2 ]

And

3B + 2(2)  = 19

3B + 4  =19     subtract  4 from each side

3B  = 15          divide  both sides  by  3

B  = 5   [a burger costs $5  ]

Note  that  every  hour  she  runs   (8  -6)  =  2 mi/hr faster

So...it  will  take  her      10 / 2   = 5  hours to lap Rob

Proof :

In 5 hours she  runs  40 miles

In 5 hours  he runs  30  miles

40   - 30    =   10 miles

The  mean is  [  300 + 700]   /  2 =  [1000 ]  / 2  =   500 miles

One standard  deviation   is  34.13%  above  the  mean =  ( 1 + .3413) (500) - 500  = 170.65

So....the z score we need  can be  computed as

[  650 - 500 ]

___________   = .2236

    670.65

The z score table associated with this  value  is   .58706

So....the probability  that he drives  more  than  650  miles  per day =  1 - .58706  ≈  41.3%

Call the  total  of the  unknown bldg heights = x

So

625  + x  + 858

____________  =     733

            5

1483  + x =  733 (5)

1483 + x  =3665   subtract  1483  from each side

x =   2182

When the  new  bldg is  added   the average  is

858  + 2182  + 885               

_________________  =   785

               5

So  the increase in the average is     785 - 733  =    52  ft

If discriminant is <0 then nonreal roots

b^2 - 4ac <0

k^2 -4(12)(27) <0

k^2 < 1296

K < 36  or >-36      (-36,36)

THX, EP!!!!

Let  the  current  rate = C

Then the rate  of the boat in still water = 5C

And   Distance  / Rate  = Time

The  effective rate withthe  current = 5C + C

The effective rate   against the current =  5C  -C

So

    12                   12

_______  +     ______   =     2 

(5C +C)           5C - C

    12                  12

   ____       +   ______  =  2

     6C                 4C

       2              6

     ___   +    ____  =    2

       C             C

           8

      _____  =    2                   multiply both sides  by  C

           C

          8  =   2C

          4  =   C    =  current rate in mph

     5C = 5 (4)   =  20  = boat rate in still water  in mph

I'm sorry to bother you, Alan, but that's wrong.

It means that   - b/2a = 4     multiply both sides by -2

   b/a = -8

Thakns, but it says its incorrect, do you mind verifying?

Thanks

If x  = 4  is  the  axis of symmetry....then  the  x coordinate of the  vertex = 4

And  the  x coordinate  of the  vertex  =  -b/a

So

4 =  -b/a

-4 =  b/a

Because  of symmetry of the  roots around the  vertex,  we can solve  for the other  x intercept thusly :

( 3 + [ 3 - - 2] , 0 )   =  (  3  + 5 , 0 )    =   (8, 0)

So....the other  x intercept  is  ( 8, 0)